Nonsmooth set variational inequality problems and optimality criteria for set optimization
Emrah Karaman · Miskolc mathematical notes/Mathematical notes · 2020
In this work, set-valued optimization problems are considered according to an order relation, which is a partial order on the family such that contains nonempty bounded sets of the space.A generalized convexity is defined for set-valued mapping by using the partial order relation.Nonsmooth variational inequality problems are introduced with the aid of M-directionally derivative.Some optimality criteria including the necessary and sufficient optimality conditions are obtained for mentioned optimization problems.